We study the satisfiability and model-checking problems for timed hyperproperties specified with HyperMITL, a timed extension of HyperLTL. While the satisfiability problem can be solved similarly as for HyperLTL, we show that the model-checking problem for HyperMITL, unless the specification is alternation-free, is undecidable even when very restricted timing constraints are allowed. On the positive side, we show that model checking HyperMITL with quantifier alternations is possible under certain semantic restrictions. As an intermediate tool, we give an ‘asynchronous’ interpretation of Wilke's monadic logic of relative distance (${\mathcal{L}}_d^{\leftrightarrow }$) and show that it characterises timed languages recognised by timed automata with silent transitions.

我们研究的满足性和模型检测问题定时hyperproperties与指定HyperMITL的定时扩展HyperLTL。虽然满足性问题可以解决同样作为HyperLTL，我们表明，该模型检测问题HyperMITL，除非该规范是交替自由，是不可判定即使在非常有限的时间限制是允许的。从积极的方面来说，我们表明在某些语义限制下，可以使用量词交替进行模型检查HyperMITL。作为中间工具，我们对威尔克的相对距离一元逻辑给出了“异步”解释（${\mathcal{升}}_d^{\leftrightarrow }$) 并表明它表征了具有无声转换的定时自动机识别的定时语言。